Thermal [1,5] hydrogen sigmatropic shifts in cis,cis-1,3-cyclononadienes probed by gas-phase kinetic studies and density functional theory calculations

The kinetics of gas-phase thermal 1,5] hydrogen shifts interconverting the five isomeric mono-deuterium-labeled cis,cis-1,3-cyclononadienes have been followed at four temperatures from 240 to 287 degrees C. The activation parameters found were Ea = 37.1 +/- 0.8 kcal/mol, log A = 11.6 +/- 0.3, DeltaH++ = 36.0 +/- 0.8 kcal/mol, and DeltaS++ = -9.0 +/- 0.3 eu. Density functional theory based calculations have provided geometries and energies for the ground-state cyclononadiene conformational isomers, for the transition states linking one to another, and for the transition states for 1,5] hydrogen shifts responsible for isomerizations among the five labeled dienes. A generalized formulation of the Winstein-Holness equation is presented and applied to the complex system, one that involves 11 ground-state conformers, 10 transition states separating them, and five transition states for 1,5] hydrogen shifts. The value for the empirical Ea derived from calculated mole fractions of ground-state conformers and calculated energies for specific ground-state conformers and 1,5] hydrogen shift transition structures was 37.5 kcal/mol, in excellent agreement with the experimentally obtained activation energy. The significance of conformational options in various ground states and transition structures for the 1,5] hydrogen shifts is considerable, an inference that may well have general applicability.